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Crane Boom

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Can someone plzzz help???

A 63.9 kg carpenter at a construction site plans to swing in a circular arc from one roof top to an adjacent roof at the end of a 10.5 meter rope suspended from a crane boom. If her wiry arms, toughened by years of driving spikes with a No. 22 framing hammer, are capable of exerting 1142 N of force on the rope, what is the maximum speed that she can tolerate at the low point of her swing?

Her arm strength equals the maximum tension she can produce in the rope. This maximum tension must support both her weight and the centripetal force she is experiencing.

What is pulling her down?
1. Weight : Constant
2. Centripetal force: varies with velocity

LEt us see how much is the constant part: her weight:
Weight = mass x accelertion due to gravity = m *g
m = 63.9 kg
g = 9.8 m/s^2

Hence weight = m*g = 63.9*9.8 = 626.22 Newtons

So the total force (tension) that she can take up is 1142 N. So the maximum force due to centripetal force = 1142 - 626.22 = 517.78 N

WE know centripetal force = v^2 * r
v = velocity and r = radius
we know r = 10.5m
therefore 517.78 = v^2 * 10.5
v^2 = 517.78/10.5 = 49.1219048
v = sqrt(49.1219048) = 7.0087 m/s

So the maximum velocity she can tolerate is 7.0087 m/s

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